Agglomerative Hierarchical Clustering for Selecting Valid Instrumental Variables
This addresses the issue of invalid IVs in econometrics, particularly for multiple endogenous regressors, but is incremental as it builds on existing techniques.
The paper tackles the problem of selecting valid instrumental variables (IVs) from a large set where some may be invalid, proposing a method that combines hierarchical clustering with a test of overidentifying restrictions and shows oracle properties if the largest group is valid. Simulation results indicate advantageous performance, and the method is applied to estimate the effect of immigration on wages.
We propose a procedure which combines hierarchical clustering with a test of overidentifying restrictions for selecting valid instrumental variables (IV) from a large set of IVs. Some of these IVs may be invalid in that they fail the exclusion restriction. We show that if the largest group of IVs is valid, our method achieves oracle properties. Unlike existing techniques, our work deals with multiple endogenous regressors. Simulation results suggest an advantageous performance of the method in various settings. The method is applied to estimating the effect of immigration on wages.